Hana sticks three pieces of coloured card onto a board: a square, a circle and a triangle. The square overlaps the circle, and the circle overlaps the triangle. The square and the triangle do not touch each other. Each overlapping part is shaded, and all the other parts of the cards are unshaded. The ratio of the area of the square to the area of the circle to the area of the triangle is 8 : 6 : 5. The shaded part where the square and the circle overlap is 13 of the area of the circle. The shaded part where the circle and the triangle overlap is 15 of the area of the triangle.
- Find the ratio of the shaded area to the unshaded area. Give your answer in the simplest form.
- The unshaded area is 91 cm². Find the area of the circle.
Need a hint?
Each shaded part belongs to two cards, so it is counted twice when you add the three card areas. Take it away once for each card it sits on.
Worked answer
- (a) Let the areas be 8 units (square), 6 units (circle) and 5 units (triangle).
- Square and circle overlap: 13 of 6 units = 2 units.
- Circle and triangle overlap: 15 of 5 units = 1 unit.
- Shaded area = 2 + 1 = 3 units.
- Total of the three card areas = 8 + 6 + 5 = 19 units. The shaded parts were counted twice, so the unshaded area = 19 − 3 − 3 = 13 units.
- Shaded : unshaded = 3 : 13, which is already in simplest form.
- (b) 13 units = 91 cm², so 1 unit = 91 ÷ 13 = 7 cm².
- Circle = 6 units = 6 × 7 = 42 cm².
Answer: 42 cm²
The mistake this question tests
Habit
Simplest form in final fraction answers
Many pupils work out the unshaded area as 19 − 3 = 16 units. But each shaded part is counted in two cards, so 3 units must be taken away twice, giving 13 units.
How to fix it at home →More PSLE ratio questions
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See the answer →Practise PSLE ratio until the mistakes stop.
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